Bayern Munich 3 Chelsea 2
It looked to be plain-sailing for Jose Mourinho's side when Frank Lampard's deflected shot gave the visitors the lead on the half-hour.
But after Claudio Pizarro's equaliser midway through the second half, the Blues had to survive a sticky spell before eventually regaining the lead through Didier Drogba's header. Bayern won the second leg thanks to last gasp-goals by Paolo Guerrero and Mehmet Scholl.
Chelsea will now play either Liverpool or Juventus in their second successive Champions League semi-final.
The opening minutes of the game were particularly lively. Drogba beat the offside trap in the second minute but Oliver Kahn was quick to see the danger and raced off his line to deny the Chelsea striker with an outstretched leg.
In the fourth minute an unmarked Michael Ballack had a goalbound shot blocked and 60 seconds later Pizarro's shot was saved by Petr Cech after Ze Roberto's pace and teasing cross had created an opening for the Peruvian.
After the lively opening Chelsea managed to take the sting out of the game and the next chance was not created until the 18th minute when German international Bastian Schweinsteiger barged his way into the penalty area but then dragged his shot wide.
Two minutes later Lampard tried his luck from the edge of the area but his shot was deflected away for a corner.
Chelsea took the lead on the half-hour when Joe Cole set up Lampard on the edge of the penalty area and the former West Ham man's shot was deflected by Lucio past Kahn and into the net.
After the goal Bayern initially responded well and Cech was just able to turn Schweinsteiger's bobbling long-range drive away for a corner in the 33rd minute.
Five minutes before the break Ballack fired a cross into the six-yard area but no Bayern player was able to get on the end of it and he then blasted a shot high and wide after Robert Huth's poor headed clearance had given the midfielder the chance.
Cech easily dealt with a speculative long-range drive by Lucio at the start of the second half but the hosts appeared to have lost the belief that they would get back into the game.
Chelsea's hard-working attitude was exemplified by Cole in the 55th minute when he got back to make an excellent tackle on Ze Roberto inside his own penalty area.
Just before the hour mark Kahn made a tremendous save to deny Damien Duff as the Blues threatened to extend their advantage.
But Bayern equalised in the 65th minute when Cech parried Ballack's bullet header on to the post and Pizarro tapped home the rebound from a matter of centimetres out.
The goal gave Bayern some added impetus and four minutes later Huth's deflected header looped on to his own crossbar and from the resulting corner Eidur Gudjohnsen cleared Ballack's header off the line.
But in the 80th minute Drogba ended Bayern's comeback when he glanced a header from Cole's accurate cross into the corner of the net and stoppage-time goals by Guerrero and Scholl proved to be mere consolation for the hosts.